R-process in Low Entropy Neutrino Driven Winds

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1 R-process in Low Entropy Neutrino Driven Winds E. Baron John J. Cowan, Tamara Rogers, 1 and Kris Gutierrez 2 Dept. of Physics and Astronomy, University of Oklahoma, 440 W. Brooks, Rm 131, Norman, OK ABSTRACT We present a parameter study which examines the r-process expected from the ejecta produced by a neutrino driven wind from the accretion induced collapse (AIC) of a white dwarf to a neutron star. The ejecta from this environment is different than that expected from the neutrino driven wind that follows the formation of a neutron star in the core collapse of a massive star which produces a Type II (or Type Ib/c) supernova. The entropy and electron fraction are significantly lower than in the shock driven supernova case. Using the results of hydrodynamical calculations as guidance, we find that for a narrow range of conditions (S 3 5and0.36 < <0.41) an r-process distribution that approximates the solar system abundances. The amount of material ejected in AIC is naturally limited to be low, M ejecta M, an amount that would be sufficient to synthesize the Galactic r-process abundances. Also there are no worries that the material will fall back onto the neutron star in AIC. Subject headings: nuclear reactions, nucleosynthesis, abundances supernovae: general white dwarfs neutron stars 1. Introduction White dwarfs in binary systems accreting material from a companion star are a common occurrence in stellar evolution. Close binaries are formed both initially and through the action of a common envelope during the giant phase of the primary and the secondary star. White dwarfs accreting material in binary systems occur observationally as cataclysmic variables, symbiotic stars and other types of variable stars. These stars are the 1 Dept. of Physics, University of Arizona, Tucson, AZ 85721;trogers@as.arizona.edu 2 Dept. of Physics, Box , Texas Tech University, Lubbock, TX ;mrground@aol.com

2 2 progenitors of classical novae (e.g.?), Type Ia supernovae (cf.?), as well as X-ray novae and supersoft sources (SSXS) (?). The response of the white dwarf to the accreted material depends on the initial mass of the white dwarf, the accretion rate, and the initial white dwarf temperature (cf.?). Most white dwarfs are initially of such low mass and accrete hydrogen at a sufficiently low rate that they develop a degenerate hydrogen shell which then presumably explodes in a classical nova. In most cases the nova explosion reduces the total white dwarf mass (e.g.?). Some white dwarfs may be able to burn hydrogen stablely, during which time they would appear as SSXS and they may grow to the Chandrasekhar mass to become progenitors of Type Ia supernovae (?). If the initial white dwarf is C/O, but its initial mass is high > 1.2 M then it is more likely to collapse to form a neutron star than to explode as a Type Ia supernova (?). O-Ne-Mg white dwarfs are formed during binary evolution of stars in the mass range 8 <M <12 M (????), most of which end up as O-Ne-Mg novae (e.g.??), but those that grow to the Chandrasekhar mass collapse to form neutron stars (?). Thus, stars in binaries with initial masses 6 <M <12 M may be expected to collapse to neutron stars due to accretion of mass onto the primary white dwarf; a process called accretion induced collapse (AIC) to distinguish it from the usual channel of neutron star formation, the core collapse supernova of a massive star. The following channels for AIC have been identified theoretically: O-Ne-Mg core formed in a high mass binary; C/O core formed in a wide binary M WD > 1.2; the merging of 2 white dwarfs, but during the merger process ignition of C-shell flashes on the more massive white dwarf burns it to O-Ne-Mg, which then collapses; in galactic globular clusters where the density is high one may merge more than 2 white dwarfs, where the initial merger leads to an O-Ne-Mg core (?). In the traditional picture the r-process is thought to be produced during a core collapse supernova (a supernova of Type II or Ib/c). This model is attractive since it satisfies the condition that the r-process be primary (?). However, the requirement that each supernova produce < 10 5 M of r-process elements seems unnatural, particularly since during the supernova a fair amount of material produced as 56 Ni may well fall back onto the forming neutron star. Recent studies have tended to focus on the production of r-process nuclei in the very high entropy environment of the neutrino driven wind blown off by the forming neutron star in core collapse supernova (?????). However, these calculations all fail to reproduce the solar r-process pattern and find that extremely high entropies per nucleon (S >400, Boltzmann s constant = 1) are required in order to produce the platinum peak (??). It is unclear whether such conditions actually occur in the formation of the neutron star (?). Here we consider the opposite regime, S 3 5. These are conditions that are

3 3 found in the ejecta produced in AIC (see below). In the high entropy regime considered in previous studies the nuclei are initially all broken up into free neutrons and protons. In this lower entropy regime, although still radiation dominated, some of the neutrons and protons are forced to remain in nuclei, since a free neutron has an entropy of S 8(?). Thus, if we consider both low conditions and low entropy conditions, the nuclei will begin as already very neutron rich and the number of neutrons per seed nucleus needed to reach the platinum peak will be reduced. 2. Description The collapse of a white dwarf to a neutron star has been studied previously by?) and?). The initial model was a 1.1 M C/O white dwarf with an accretion rate of M yr 1 which grew to 1.40 M and collapsed (?). While?) found no mass ejection, with finer zoning and more accurate neutrino transport?) found that the very outermost layers of the star are ejected in a neutrino driven wind. In their direct calculations?) found that the ejected mass was in the range M <M ejecta < M. The electron fraction in the directly ejected material was in the range 0.1 < <0.5. However, the final of the ejected material is not expected to remain so low due to neutrino capture on free nucleons driving toward 0.5. In a parameterized post-processing?) found ejected values of 0.44 < <0.5 (see their Figure 5). To reliably calculate the final ejected requires an accurate knowledge of the emitted neutrino and anti-neutrino spectrum and accurate radiation transport of the neutrinos from the neutrinosphere through the optically thin ejected wind. In this paper, we examine the calculated ejecta from the results of?) and for a variety of values. We follow the material as it expands through NSE and then follow its production of r-process elements. Taking conditions directly from the results of?) we expanded the material adiabatically (by numerically integrating the first law of thermodynamics) until the temperature reached K. Above this temperature the material remains in nuclear statistical equilibrium (NSE) and hence the use of an NSE equation of state is well justified. The equation of state used in?) is the mean nucleus EOS of Cooperstein and Baron (??). Since we wished to follow the distribution of nuclei actually produced in NSE, we also used an equilibrium network which included 1404 known nuclei. This then produced a distribution of nuclei. The resulting compositions were then followed through expansion using the code SNBLAST (?) with an exponential expansion timescale of 1 s. The nuclear reactions were followed for 1000 s. The results using a single mean nucleus were comparable to those using a full distribution of nuclei, although the higher mass numbers in the r-process were more difficult

4 4 to attain than in the case with a single mean nucleus and the distribution is preferred since it is more physical. The expansion timescale that we use is in accord with the results of?) who estimate the r-process timescale to be in the range s and with those of?) who find a timescale of s. These timescales are significantly longer than the expansion timescale determined by?), who find timescales as short as 5 ms, which seems far too short compared to the nuclear timescales. This discrepancy may simply a matter of definition and will be addressed in future work. Figure 1 displays the initial distribution of nuclei in the (Z,A) plane for =0.41. While there is a significant fraction of free neutrons and alpha particles, there is also a large fraction of iron-peak nuclei, including very neutron rich species such as 48 Ca. Figure 2 displays the results after nuclear reactions have stopped for the electron fraction in the range , compared to the solar r-process abundances. The results agree reasonably well with the solar values. In all the models, the three r-process peaks tend to peak at slightly higher mass numbers than in the solar nebula. This may be the result of an inadequate (i.e. too low) neutron number density, or it may have resulted from using older and more uncertain nuclear data (e.g. cross sections). R-process calculations using more recent and more accurate data (see e.g.?) will be needed to determine the cause of the offsets in the predicted r-process peaks. We note, however, the low entropy that we use in the current calculations will not represent all of the ejected material and the entropy will rise at later times. This higher entropy material has been examined by?) who followed the r-process of the parameterized post-processed material in the calculations of?).?) found that this post-processed material with S 20 pollutes the ISM in neutron rich species. We note that here we have focused on the results directly from the hydrodynamical calculations of?) rather than the post-processed material in that calculation. Because the neutrino transport is schematic in both the direct hydrodynamic and the post-processing calculations of?) both our present calculations and those of?) should be followed up with more detailed calculations. Also?) begin with a mixture of only free neutrons and protons, rather than with the large equilibrium network we employ here. In a future work where the final electron fraction is better determined it will be worthwhile to integrate the entire produced r-process over the range of ejected conditions, but our preliminary results are promising. Since the observed r-process abundances (see below) point to a unique set of conditions and the low entropy parameters we have examined here are promising, it seems fruitful to determine whether these conditions can be obtained in detailed hydrodynamical calculations.

5 5 3. Discussion and Conclusions AIC is expected to occur stars in binaries with initial primary mass 6 <M <12 M where the upper and lower ends of the range are uncertain. This is just the mass range that has been found to be of interest for the production of the r-process (??).?) and?) found that a time delay for r-process production of 10 8 yr could account for the delay in the production of europium compared to that of iron (?). These authors found using [Fe/H] as a time axis, that the [Eu/Fe] ratio was better fit by a model where the Eu is produced with a small time delay compared to that of the initial production of Fe. They interpreted this data to imply that the initial production of Fe in our galaxy is due to SNe II in massive stars M > 15 M and that the r-process is produced in stars with masses in the range 8 11 M. Since AIC naturally occurs in binary stars of this mass range and since the mass range is favored by the IMF, this holds promise for our model. While the total ejected mass in AIC is uncertain, it is almost certainly in the range M (?). The frequency of AIC in the galaxy is also uncertain, especially since it is possible that the merging of double degenerate stars produces AIC rather than SNe Ia (?). Population synthesis studies predict AIC rates in the range yr 1 (??). Over a galactic age of yr, this would produce a total r-process mass of M, well within the observed galactic r-process abundance of 10 4 M (?).?) have argued that a single r-process is inconsistent with the meteoritic data and that a uniform r-process would grossly overproduce 129 Iand 107 Pd. They further argue that there should be diverse r-process sources, one of which produces mass numbers A<140 and the other is responsible for A>140.?) argue that in order to account for the 129 I and 182 Hf data a minimal scenario would require 2 r-process events one which occurs every 10 7 yr (in a region 100 pc in radius in the Galaxy) and primarily produces nuclei with A 195 and in particular almost no 129 I. They suggest that the other process occurs roughly every 10 8 yr and produces most of the rest of the r-process, excluding those in the A 195 peak, particularly 182 Hf. On the other hand, the stellar abundance distribution from Ba through the third r-process peak in the Galactic halo stars is consistent with the solar system r-process abundance curve (??). These data strongly suggest that the heaviest neutron-capture elements are made in the same r-process site. Furthermore, the presence of these elements, including Hf and Pt (?), in the oldest, Galactic metal-poor stars demands a rapid stellar evolutionary timescale for this r-process site. The stellar elemental data are incomplete below Ba (A 135), and in particular, there are no detections of I in any halo stars. While there are several possible explanations of the lighter neutron-capture abundance detections in the halo stars, based upon the stellar data, it is unclear at this point what process is responsible for synthesizing the neutron-capture elements below Ba.

6 6 We note that in our models as falls the A 130 peak is reduced with respect to the A 195 peak and thus, it may be that very neutron-rich nuclei are ejected more frequently, and that in rare events the ejecta is more nearly neutron-proton symmetric due to differing neutrino fluxes during the formation of the neutron star. We note that examining detailed predictions (such as the Hf/I ratio) is beyond the scope of the current work, since the ejecta conditions remain uncertain. In future work we will address these and other more detailed questions. Our models show that the conditions produced in AIC are extremely promising as an astrophysical site for the r-process. The low entropies of the ejecta guarantee that the initial conditions for the r-process consists of free neutrons with a significant mass fraction of extremely neutron rich nuclei. These conditions naturally lead to a build up of r-process nuclei all the way to the Pt peak. Additionally, the mass range of AIC progenitors is at the lower end of massive stars and involves binary interaction which leads to a natural time delay in the production of r-process elements compared to the production of iron in SNe II of massive stars. Our work of course does not preclude massive stars as an additional r-process site. In view of the apparent need for a very recent injection of A 195 material in the solar system, it is possible that this part of the r-process is produced by massive stars, and the rest of the r-process is produced in accretion induced collapse. To obtain definitive answers to the r-process site will clearly involve a solution of the core-collapse problem, which does not yet appear to be in sight (??). We thank Al Cameron for stimulating discussions and encouragement. This work was supported in part by NSF grants AST , AST , NASA grant NAG and an IBM SUR grant to the University of Oklahoma. T. R. and K. G. were partially supported by an NSF REU supplement. Some of the calculations presented in this paper were performed at the San Diego Supercomputer Center (SDSC), the Cornell Theory Center (CTC), and at the National Center for Supercomputing Applications (NCSA), with support from the National Science Foundation, and at the NERSC with support from the DoE. We thank all these institutions for a generous allocation of computer time.

7 7 Fig. 1. The initial abundances of nuclei in nuclear statistical equilibrium displayed in the (Z,A) plane. The dotted line delimits the case of symmetric nuclei Z = A/2 and is intended to guide the eye. These data are available from baron/rprocs abunds.dat.

8 8 log 10 (abundance) + constant Solar = 0.36 = 0.37 = 0.38 = 0.39 = 0.40 = A Fig. 2. The calculated abundances for are compared to the solar abundance curve (upper curve).

STELLAR HEAVY ELEMENT ABUNDANCES AND THE NATURE OF THE R-PROCESSR. JOHN COWAN University of Oklahoma

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